A derivation of conditional cumulants in exponential models

Shaul K. Bar-Lev

doi:10.1080/00031305.1994.10476040

A derivation of conditional cumulants in exponential models

Shaul K. Bar-Lev

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let T = (T₁, …, T_k, k ≥ 2) be a minimal sufficient statistic for a k-parameter natural exponential model. Consider a partition of T into (T₁, T₂), where T₁ = (T₁, …, T_r) and T₂ = (T_r+1, …, T_k; 1 ≤ r < k). It is shown that cumulants of the conditional distribution of T₁, given T₂ = t₂, can be computed through the marginal distribution of T₂ and the norming constant that makes the model a probability model. The results are illustrated by a few examples.

Original language	English
Pages (from-to)	126-129
Number of pages	4
Journal	American Statistician
Volume	48
Issue number	2
DOIs	https://doi.org/10.1080/00031305.1994.10476040
State	Published - May 1994

Keywords

Conditional moments
Natural exponential family

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1080/00031305.1994.10476040

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abstract = "Let T = (T1, …, Tk, k ≥ 2) be a minimal sufficient statistic for a k-parameter natural exponential model. Consider a partition of T into (T1, T2), where T1 = (T1, …, Tr) and T2 = (Tr+1, …, Tk; 1 ≤ r < k). It is shown that cumulants of the conditional distribution of T1, given T2 = t2, can be computed through the marginal distribution of T2 and the norming constant that makes the model a probability model. The results are illustrated by a few examples.",

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AB - Let T = (T1, …, Tk, k ≥ 2) be a minimal sufficient statistic for a k-parameter natural exponential model. Consider a partition of T into (T1, T2), where T1 = (T1, …, Tr) and T2 = (Tr+1, …, Tk; 1 ≤ r < k). It is shown that cumulants of the conditional distribution of T1, given T2 = t2, can be computed through the marginal distribution of T2 and the norming constant that makes the model a probability model. The results are illustrated by a few examples.

KW - Conditional moments

KW - Natural exponential family

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JF - American Statistician

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ER -

A derivation of conditional cumulants in exponential models

Abstract

Keywords

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